Shifted analogues of the divisor function

Abstract: Suppose that $\theta$ is irrational. Then almost all elements $\nu\in \mathbb Z[\theta]$ that may be written as a $k$-fold product of the shifted integers $n+\theta$ $(n\in \mathbb N)$ are thus represented essentially uniquely. We discuss this and related paucity problems.

Most of this work is joint with Winston Heap and Anurag Sahay.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)